Germany had hoped to call on the world number five for the play-off against Latvia as they look to preserve their World Group place – Jens Gerlach's team having lost 4-0 to Belarus in the quarter-finals.
However, the German Tennis Federation confirmed Kerber will not fly with the team to Riga due to illness.
"I am disappointed and sad that I have to cancel the Fed Cup match against Latvia for health reasons," said Kerber.
"Unfortunately, after a delayed flu, I did not get a medical clearance and had to take a break for the next few days.
"Even though I cannot be there, I am in contact with the team and I am sure that the girls will prevail in the relegation [play-off]."
Kerber will hope the flu does not keep her sidelined for too long as she looks to complete a career Grand Slam at next month's French Open.